This seminar addresses bachelor and master students interested in the analysis and numerical analysis of geometric partial differential equations (GPDEs) and surface PDEs. We will introduce basic GPDEs and SPDEs, discuss their well-posedness and numerical discretization. In particular, surface finite element methods will be analyzed.  The main literature will be

Deckelnick, Klaus, Gerhard Dziuk, and Charles M. Elliott. "Computation of geometric partial differential equations and mean curvature flow." Acta numerica 14 (2005): 139-232.

Dziuk, Gerhard, and Charles M. Elliott. "Finite element methods for surface PDEs." Acta Numerica 22 (2013): 289-396.

Dziuk, Gerhard, and Charles M. Elliott. "Surface finite elements for parabolic equations." Journal of Computational Mathematics (2007): 385-407.

Basic knowledge on PDEs and their numerical solution using finite element method (Num 3) is desired.